Abstract
Theorem 12.1 is formulated in [72] as follows:
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Theorem 1.
For integers h, k with (h, k) = 1, let \( \lambda \left( {h/k} \right) = {\left( {2k} \right)^{{ - 1}}}\sum\nolimits_{{q = 1}}^{{2k}} {{e^{{2\pi ih{q^{2}}/2k}}}} \) and set \( {A_{k}} = \sum\nolimits_{{1 \le h \le 2k,\left( {h,k} \right) = 1}} {{\lambda ^{s}}{e^{{ - 2\pi ihn/2k}}}} \). Then, if \( S\left( n \right) = \sum\nolimits_{{k = 1}}^{\infty } {{A_{k}}} \) and s = 5, 6, 7, or 8, one has for some constant c = c(s), independent of n, that
$${r_{s}}\left( n \right) = c\left( s \right){n^{{\left( {s/2} \right) - 1}}}S\left( n \right) $$.
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© 1985 Springer-Verlag New York Inc.
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Grosswald, E. (1985). Alternative Methods for Evaluating r s (n). In: Representations of Integers as Sums of Squares. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8566-0_14
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DOI: https://doi.org/10.1007/978-1-4613-8566-0_14
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